Abstract
In this paper, we study a nonlocal boundary value problem for a second-order Hahn difference equation. Our problem contains two Hahn difference operators with different numbers of q and ω. An existence and uniqueness result is proved by using the Banach fixed point theorem, and the existence of a positive solution is established by using the Krasnoselskii fixed point theorem.
Highlights
The quantum calculus, known as the calculus without considering limits, deals with sets of nondifferentiable functions
There are many different types of quantum difference operators, for example, the Jackson q-difference operator, the forward difference operator, the backward difference operator, and so on. These operators are found in many applications of mathematical areas such as orthogonal polynomials, basic hypergeometric functions, combinatorics, the calculus of variations, the theory of relativity, hypergeometric series, complex analysis, particle physics, and quantum mechanics
The Hahn difference operator is generalized to two well-known difference operators, the forward difference operator and the Jackson q-difference operator
Summary
The quantum calculus, known as the calculus without considering limits, deals with sets of nondifferentiable functions. In , Malinowska and Martins [ ] studied the generalized transversality conditions for the Hahn quantum variational calculus. In Section , we prove the existence and uniqueness of a solution to problem In Sections - , we establish some properties of the Green function and the existence of a positive solution to problem Hahn difference of f is defined by f (qt + ω) – f (t) Dq,ωf (t) = t(q – ) + ω for t = ω and Dq,ωf (ω ) = f (ω ), provided that f is differentiable at ω. The following lemma is the fundamental theorem of Hahn calculus. By the Banach fixed point theorem, F has a fixed point, which is a unique solution of problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
